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Graphs which are linked cycles

Adams, Peter and Eggleton, Roger and MacDougall, James A. (2009) Graphs which are linked cycles. Congressus Numerantium, 195 .

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Abstract

A graph H of order h is an n-linked cycle if it has an induced subgraph G of order g < h and an automorphism α: H � H of order n � 2 such that H = �{αr(G) : 0 � r < n} and G has an induced subgraph K of order k < g such that αr(G) � αr�¹(G) � K for 0 � r < n. Then G is the initial link of this linked cycle, K is its kernel, α|G is the link isomorphism, and any pair (G, α) allowing H to be expressed as a linked cycle yields a generalized factorization of H. For a given standard ordering of all finite graphs, the "earliest" pair (G, α) is a fundamental representation of H. There are 2 593 574 linked cycles among all graphs of order h � 10. The paper gives an overview, and a fundamental representation of each of them is provided on a supporting website.

Item Type: Article
Uncontrolled Keywords: graph automorphism, factorization, linked cycle
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 28 Sep 2012 12:05
URI: http://docserver.carma.newcastle.edu.au/id/eprint/1154

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